Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, November 10, 2009, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Andrei Giurgiu

Schöning discovered a simple local-search randomized algorithm for solving k-SAT, which still remains one of the fastest algorithms known so far. We recall the analysis of this algorithm using random walks on the integers, and then introduce a modified version and generalize the analysis so that it applies for the modification as well. Schöning's algorithm chooses an assignment for the variables at random, and then, as long as it is not satisfying, picks a violated clause and flips the value of a variable from that clause. If after a linear number of iterations, a satisfying assignment is still not found, the procedure is restarted. The modification consists of randomly flipping each variable that appears in the chosen violated clause. In both Schöning's algorithm and the modified version the part describing exactly which violated clause to select is left unspecified. We call that part selection rule. We produce worst-case sets of formulas which show that the analysis is tight, for two different selection rules. In the final chapter, we consider computationally un-bounded selection rules that ensure a polynomial runtime of Schöning's algorithm, and we prove that such selection rules exist for some classes of formulas. During our investigations, we also develop more general combinatorial tools which may prove useful for analyzing algorithms using random walks.

Thesis supervised by E. Welzl and R. Moser.

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